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The polynomial $2 x^{3} + k x^{2} - 5 x - 6$ is exactly divisible by $(x + 1)$ . What is the value of $k$ ?

Competition practiceAlgebra

A3
B-3
C9
D1

Step-by-Step Solution

By the factor theorem

p (- 1) = 0 : 2 (- 1)^{3} + k (- 1)^{2} - 5 (- 1) - 6 = - 2 + k + 5 - 6 = k - 3 = 0

, so

k = 3

.

Answer: A) 3

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